Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5

Question

feet and a standard deviation of 0.5
feet. A sample of 51
men’s step lengths is taken.
Step 1 of 2: Find the probability that an individual man’s step length is less than 1.9
feet. Round your answer to 4
decimal places, if necessary.

Answer 1

To find the probability that an individual man's step length is less than 1.9 feet, we need to standardize the value and then look it up in the standard normal distribution table.

First, we need to calculate the z-score:

z = (X - μ) / σ
where X is the value we are trying to find the probability for, μ is the mean, and σ is the standard deviation.

z = (1.9 - 2.5) / 0.5
z = -0.6 / 0.5
z = -1.2

Now we look up the z-score of -1.2 in the standard normal distribution table to find the probability.

From the z-score table, the probability corresponding to a z-score of -1.2 is approximately 0.1151.

Therefore, the probability that an individual man's step length is less than 1.9 feet is 0.1151.